Outlook App vs Online Outlook

This question pertains to working with Outlook on my PC/Laptop:

When using Outlook online, I am signed in using my company email, I am getting the calendar events  just fine but no emails.  The opposite happens if I use the Desktop Outlook app: I get the emails but no calendar events.  What am I possibly doing wrong??  Edit: When I hover the account manager, and Outlook email appears under my name "outlook_D80E072AF8B*****@outlook.com"

When using the app on my phone, I get the emails but no calendar events.